rippling·Software Engineer·Technical Phone Screen·Senior

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Apr 2026

Summary

Rippling SWE interview that went deep into numerical optimization theory. One question, but it had four parts and honestly felt like a mini take-home crammed into a live session. Not what I expected from a software engineering round.

Questions Asked (1)

You have a black-box convex function on a closed interval and a fixed budget of K queries (no gradients available). Describe an algorithm to find the minimum as accurately as possible, explain why gradient-based methods don't apply here, analyze how many evaluations you need to get the uncertainty interval below epsilon, and discuss how noisy observations would affect things.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

Four-parter disguised as one question.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem setup and then present the golden-section search algorithm as the optimal method for finding the minimum of a convex function using only function evaluations. Explain why gradient-based methods are inapplicable due to the black-box nature, analyze the convergence rate to achieve an uncertainty interval below epsilon, and discuss how noise would necessitate robust or stochastic optimization techniques.

Pro tip: Mention that golden-section search is optimal in the worst case for this problem, and that with noise, one can use repeated evaluations or stochastic approximation methods like Robbins-Monro, showing awareness of practical constraints.

1. Clarify problem and assumptions

Restate the problem: minimize a convex function on a closed interval using at most K function evaluations, no gradients. Confirm that the function is deterministic and that we need to output an interval containing the minimum.

2. Choose algorithm: golden-section search

Describe the golden-section search algorithm: iteratively narrow the interval by evaluating at two interior points, using the golden ratio to maintain a constant reduction factor per iteration.

3. Explain why gradient-based methods fail

Gradient-based methods require gradient information, which is unavailable in a black-box setting. Additionally, numerical differentiation would require extra evaluations and may be inaccurate, especially with noise.

4. Analyze query complexity

Derive the number of evaluations needed to reduce the interval length below epsilon. Golden-section search reduces the interval by a factor of about 0.618 per evaluation, so K ≈ log(epsilon / (b-a)) / log(0.618) evaluations are needed.

5. Discuss noisy observations

With noise, function evaluations are stochastic. Simple golden-section search may fail; instead, use repeated evaluations at each point to average out noise, or employ stochastic approximation methods. The uncertainty interval will be larger for the same budget, and convergence guarantees become probabilistic.

Key Points to Mention

Golden-section search is optimal for deterministic convex functions with no gradients.
Gradient-based methods require gradient information, which is not available; numerical gradients are costly and noisy.
Query complexity: O(log(1/epsilon)) evaluations to achieve epsilon-accuracy.
Noise necessitates robust techniques like averaging or stochastic approximation (e.g., Robbins-Monro).
Trade-off: more evaluations improve accuracy but increase cost; with noise, accuracy is limited by variance.
Alternative methods: ternary search (similar but less efficient), Fibonacci search (optimal for fixed K).

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.